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Your data matches 21 different statistics following compositions of up to 3 maps.
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Matching statistic: St000071
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(load all 2 compositions to match this statistic)
Mp00209: Permutations —pattern poset⟶ Posets
St000071: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St000071: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => ([],1)
=> 1
[1,2] => ([(0,1)],2)
=> 1
[2,1] => ([(0,1)],2)
=> 1
[1,2,3] => ([(0,2),(2,1)],3)
=> 1
[1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[3,2,1] => ([(0,2),(2,1)],3)
=> 1
[1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 4
[2,3,1,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> 8
[2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[3,1,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> 8
[3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 4
[3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
[1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> 9
[1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> 9
[1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> 9
[1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 6
[1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> 9
[1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> 12
[1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> 16
[1,3,4,5,2] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> 9
[1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> 26
[1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> 16
[1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> 16
[1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> 26
[1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> 11
[1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> 18
[1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> 14
Description
The number of maximal chains in a poset.
Matching statistic: St000909
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00209: Permutations —pattern poset⟶ Posets
St000909: Posets ⟶ ℤResult quality: 33% ●values known / values provided: 33%●distinct values known / distinct values provided: 40%
St000909: Posets ⟶ ℤResult quality: 33% ●values known / values provided: 33%●distinct values known / distinct values provided: 40%
Values
[1] => ([],1)
=> 1
[1,2] => ([(0,1)],2)
=> 1
[2,1] => ([(0,1)],2)
=> 1
[1,2,3] => ([(0,2),(2,1)],3)
=> 1
[1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[3,2,1] => ([(0,2),(2,1)],3)
=> 1
[1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 4
[2,3,1,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> 8
[2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[3,1,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> 8
[3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 4
[3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
[1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 6
[1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,4,5,2] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,5,3,2] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
[2,1,3,4,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
[2,1,3,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,4,3,5] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,4,5,3] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,5,3,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,5,4,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> 7
[2,3,1,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,1,5,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,4,1,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,4,5,1] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
[2,3,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,5,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,5,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,1,3,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,1,4,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,10),(1,11),(1,12),(2,7),(2,11),(2,12),(3,7),(3,9),(3,10),(4,6),(4,10),(4,12),(5,6),(5,9),(5,11),(6,14),(7,13),(9,13),(9,14),(10,13),(10,14),(11,13),(11,14),(12,13),(12,14),(13,8),(14,8)],15)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,4,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,4,3,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[3,1,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[3,1,2,5,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[3,1,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[3,1,4,5,2] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[3,1,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[3,1,5,4,2] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[3,2,1,4,5] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 6
[3,2,1,5,4] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> 7
[3,2,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[3,2,4,5,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[3,2,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ? ∊ {9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[3,4,5,1,2] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> 7
[3,4,5,2,1] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 6
[4,3,2,1,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
[4,5,1,2,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> 7
[4,5,3,2,1] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
[5,1,2,3,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
[5,4,1,2,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 6
[5,4,3,1,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
Description
The number of maximal chains of maximal size in a poset.
Matching statistic: St000363
Values
[1] => ([],1)
=> ([],1)
=> 1
[1,2] => ([(0,1)],2)
=> ([],2)
=> 1
[2,1] => ([(0,1)],2)
=> ([],2)
=> 1
[1,2,3] => ([(0,2),(2,1)],3)
=> ([],3)
=> 1
[1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2
[2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2
[2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2
[3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2
[3,2,1] => ([(0,2),(2,1)],3)
=> ([],3)
=> 1
[1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1
[1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 3
[1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> 5
[1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> 5
[1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> 5
[1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 3
[2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 3
[2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> 4
[2,3,1,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> 5
[2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 3
[2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ([(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {8,8}
[2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> 5
[3,1,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> 5
[3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ([(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {8,8}
[3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 3
[3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> 5
[3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> 4
[3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 3
[4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 3
[4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> 5
[4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> 5
[4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> 5
[4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 3
[4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1
[1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 1
[1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(2,7),(3,6),(3,9),(4,5),(4,7),(4,8),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(2,7),(3,6),(3,9),(4,5),(4,7),(4,8),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(2,7),(3,6),(3,9),(4,5),(4,7),(4,8),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(2,7),(3,6),(3,9),(4,5),(4,7),(4,8),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(2,5),(3,6),(3,9),(4,7),(4,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ([(2,3),(3,7),(3,11),(4,5),(4,6),(4,10),(4,11),(5,6),(5,9),(5,11),(6,8),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,4,5,2] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(2,7),(3,6),(3,9),(4,5),(4,7),(4,8),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(2,3),(3,9),(4,9),(4,11),(4,12),(4,13),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,12),(6,13),(7,8),(7,10),(7,11),(7,13),(8,10),(8,11),(8,12),(9,11),(9,12),(9,13),(10,11),(10,12),(10,13),(11,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(2,3),(2,11),(3,10),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,10),(6,7),(6,8),(6,11),(7,8),(7,9),(7,10),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ([(2,3),(3,7),(3,11),(4,5),(4,6),(4,10),(4,11),(5,6),(5,9),(5,11),(6,8),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(2,3),(3,9),(4,9),(4,11),(4,12),(4,13),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,12),(6,13),(7,8),(7,10),(7,11),(7,13),(8,10),(8,11),(8,12),(9,11),(9,12),(9,13),(10,11),(10,12),(10,13),(11,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(2,3),(2,10),(3,9),(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(5,10),(6,7),(6,9),(6,10),(7,8),(7,10),(8,10),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(2,3),(2,12),(3,11),(4,5),(4,6),(4,7),(4,8),(4,12),(5,6),(5,8),(5,10),(5,11),(6,8),(6,9),(6,11),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ([(2,3),(3,10),(4,5),(4,8),(4,9),(5,7),(5,9),(6,7),(6,8),(6,9),(6,10),(7,8),(7,10),(8,10),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,5,3,2] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(2,3),(2,10),(3,9),(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(5,10),(6,7),(6,9),(6,10),(7,8),(7,10),(8,10),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(2,7),(3,6),(3,9),(4,5),(4,7),(4,8),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(2,3),(2,11),(3,10),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,10),(6,7),(6,8),(6,11),(7,8),(7,9),(7,10),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(2,3),(2,12),(3,11),(4,5),(4,6),(4,7),(4,8),(4,12),(5,6),(5,8),(5,10),(5,11),(6,8),(6,9),(6,11),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(2,3),(2,12),(3,11),(4,5),(4,6),(4,7),(4,8),(4,12),(5,6),(5,8),(5,10),(5,11),(6,8),(6,9),(6,11),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(2,3),(2,10),(3,9),(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(5,10),(6,7),(6,9),(6,10),(7,8),(7,10),(8,10),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,3,4,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,3,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(2,3),(3,9),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,9),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,4,3,5] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(2,5),(3,6),(3,9),(4,7),(4,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,4,5,3] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(2,3),(3,10),(4,6),(4,7),(4,8),(5,6),(5,8),(5,9),(5,10),(6,7),(6,9),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,5,3,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(2,3),(3,10),(4,6),(4,7),(4,8),(5,6),(5,8),(5,9),(5,10),(6,7),(6,9),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,5,4,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,1,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(2,7),(3,6),(3,9),(4,5),(4,7),(4,8),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,1,5,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(2,3),(3,10),(4,6),(4,7),(4,8),(5,6),(5,8),(5,9),(5,10),(6,7),(6,9),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,4,1,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(2,7),(3,6),(3,9),(4,5),(4,7),(4,8),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,4,5,1] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(2,3),(3,11),(4,6),(4,9),(4,10),(4,11),(5,7),(5,8),(5,10),(5,11),(5,12),(6,8),(6,9),(6,10),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,11),(8,12),(9,10),(9,12),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,5,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(2,3),(2,10),(3,9),(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(5,10),(6,7),(6,9),(6,10),(7,8),(7,10),(8,10),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(2,3),(3,9),(4,9),(4,11),(4,12),(4,13),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,12),(6,13),(7,8),(7,10),(7,11),(7,13),(8,10),(8,11),(8,12),(9,11),(9,12),(9,13),(10,11),(10,12),(10,13),(11,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
=> ([(2,3),(3,13),(4,5),(4,6),(4,11),(4,12),(4,13),(5,6),(5,10),(5,11),(5,13),(6,9),(6,11),(6,13),(7,8),(7,9),(7,10),(7,12),(7,13),(8,9),(8,10),(8,12),(8,13),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(2,3),(2,12),(3,11),(4,5),(4,6),(4,7),(4,8),(4,12),(5,6),(5,8),(5,10),(5,11),(6,8),(6,9),(6,11),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(2,3),(2,12),(3,11),(4,5),(4,6),(4,7),(4,8),(4,12),(5,6),(5,8),(5,10),(5,11),(6,8),(6,9),(6,11),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,5,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ([(2,3),(3,12),(4,7),(4,9),(4,11),(4,12),(5,6),(5,8),(5,10),(5,12),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(2,3),(2,11),(3,10),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,10),(6,7),(6,8),(6,11),(7,8),(7,9),(7,10),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,1,3,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(2,3),(3,11),(4,6),(4,9),(4,10),(4,11),(5,7),(5,8),(5,10),(5,11),(5,12),(6,8),(6,9),(6,10),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,11),(8,12),(9,10),(9,12),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,1,4,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ([(2,3),(3,12),(4,7),(4,9),(4,11),(4,12),(5,6),(5,8),(5,10),(5,12),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,10),(1,11),(1,12),(2,7),(2,11),(2,12),(3,7),(3,9),(3,10),(4,6),(4,10),(4,12),(5,6),(5,9),(5,11),(6,14),(7,13),(9,13),(9,14),(10,13),(10,14),(11,13),(11,14),(12,13),(12,14),(13,8),(14,8)],15)
=> ([(2,3),(2,14),(3,13),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(5,6),(5,7),(5,8),(5,10),(5,12),(5,13),(5,14),(6,7),(6,8),(6,10),(6,11),(6,13),(6,14),(7,8),(7,9),(7,11),(7,13),(7,14),(8,9),(8,12),(8,13),(8,14),(9,10),(9,11),(9,12),(9,13),(10,11),(10,12),(10,13),(11,12),(11,14),(12,14),(13,14)],15)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(2,3),(2,12),(3,11),(4,5),(4,6),(4,7),(4,8),(4,12),(5,6),(5,8),(5,10),(5,11),(6,8),(6,9),(6,11),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,4,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(2,3),(3,11),(4,6),(4,9),(4,10),(4,11),(5,7),(5,8),(5,10),(5,11),(5,12),(6,8),(6,9),(6,10),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,11),(8,12),(9,10),(9,12),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,4,3,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(2,7),(3,6),(3,9),(4,5),(4,7),(4,8),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[3,1,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(2,7),(3,6),(3,9),(4,5),(4,7),(4,8),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 1
Description
The number of minimal vertex covers of a graph.
A '''vertex cover''' of a graph $G$ is a subset $S$ of the vertices of $G$ such that each edge of $G$ contains at least one vertex of $S$. A vertex cover is minimal if it contains the least possible number of vertices.
This is also the leading coefficient of the clique polynomial of the complement of $G$.
This is also the number of independent sets of maximal cardinality of $G$.
Matching statistic: St001304
Values
[1] => ([],1)
=> ([],1)
=> 1
[1,2] => ([(0,1)],2)
=> ([],2)
=> 1
[2,1] => ([(0,1)],2)
=> ([],2)
=> 1
[1,2,3] => ([(0,2),(2,1)],3)
=> ([],3)
=> 1
[1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2
[2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2
[2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2
[3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2
[3,2,1] => ([(0,2),(2,1)],3)
=> ([],3)
=> 1
[1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1
[1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 3
[1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> 5
[1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> 5
[1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> 5
[1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 3
[2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 3
[2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> 4
[2,3,1,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> 5
[2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 3
[2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ([(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {8,8}
[2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> 5
[3,1,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> 5
[3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ([(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {8,8}
[3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 3
[3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> 5
[3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> 4
[3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 3
[4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 3
[4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> 5
[4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> 5
[4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> 5
[4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 3
[4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1
[1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 1
[1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(2,7),(3,6),(3,9),(4,5),(4,7),(4,8),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(2,7),(3,6),(3,9),(4,5),(4,7),(4,8),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(2,7),(3,6),(3,9),(4,5),(4,7),(4,8),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(2,7),(3,6),(3,9),(4,5),(4,7),(4,8),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(2,5),(3,6),(3,9),(4,7),(4,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ([(2,3),(3,7),(3,11),(4,5),(4,6),(4,10),(4,11),(5,6),(5,9),(5,11),(6,8),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,4,5,2] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(2,7),(3,6),(3,9),(4,5),(4,7),(4,8),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(2,3),(3,9),(4,9),(4,11),(4,12),(4,13),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,12),(6,13),(7,8),(7,10),(7,11),(7,13),(8,10),(8,11),(8,12),(9,11),(9,12),(9,13),(10,11),(10,12),(10,13),(11,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(2,3),(2,11),(3,10),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,10),(6,7),(6,8),(6,11),(7,8),(7,9),(7,10),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ([(2,3),(3,7),(3,11),(4,5),(4,6),(4,10),(4,11),(5,6),(5,9),(5,11),(6,8),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(2,3),(3,9),(4,9),(4,11),(4,12),(4,13),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,12),(6,13),(7,8),(7,10),(7,11),(7,13),(8,10),(8,11),(8,12),(9,11),(9,12),(9,13),(10,11),(10,12),(10,13),(11,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(2,3),(2,10),(3,9),(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(5,10),(6,7),(6,9),(6,10),(7,8),(7,10),(8,10),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(2,3),(2,12),(3,11),(4,5),(4,6),(4,7),(4,8),(4,12),(5,6),(5,8),(5,10),(5,11),(6,8),(6,9),(6,11),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ([(2,3),(3,10),(4,5),(4,8),(4,9),(5,7),(5,9),(6,7),(6,8),(6,9),(6,10),(7,8),(7,10),(8,10),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,5,3,2] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(2,3),(2,10),(3,9),(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(5,10),(6,7),(6,9),(6,10),(7,8),(7,10),(8,10),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(2,7),(3,6),(3,9),(4,5),(4,7),(4,8),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(2,3),(2,11),(3,10),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,10),(6,7),(6,8),(6,11),(7,8),(7,9),(7,10),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(2,3),(2,12),(3,11),(4,5),(4,6),(4,7),(4,8),(4,12),(5,6),(5,8),(5,10),(5,11),(6,8),(6,9),(6,11),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(2,3),(2,12),(3,11),(4,5),(4,6),(4,7),(4,8),(4,12),(5,6),(5,8),(5,10),(5,11),(6,8),(6,9),(6,11),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(2,3),(2,10),(3,9),(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(5,10),(6,7),(6,9),(6,10),(7,8),(7,10),(8,10),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,3,4,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,3,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(2,3),(3,9),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,9),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,4,3,5] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(2,5),(3,6),(3,9),(4,7),(4,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,4,5,3] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(2,3),(3,10),(4,6),(4,7),(4,8),(5,6),(5,8),(5,9),(5,10),(6,7),(6,9),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,5,3,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(2,3),(3,10),(4,6),(4,7),(4,8),(5,6),(5,8),(5,9),(5,10),(6,7),(6,9),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,5,4,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,1,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(2,7),(3,6),(3,9),(4,5),(4,7),(4,8),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,1,5,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(2,3),(3,10),(4,6),(4,7),(4,8),(5,6),(5,8),(5,9),(5,10),(6,7),(6,9),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,4,1,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(2,7),(3,6),(3,9),(4,5),(4,7),(4,8),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,4,5,1] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(2,3),(3,11),(4,6),(4,9),(4,10),(4,11),(5,7),(5,8),(5,10),(5,11),(5,12),(6,8),(6,9),(6,10),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,11),(8,12),(9,10),(9,12),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,5,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(2,3),(2,10),(3,9),(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(5,10),(6,7),(6,9),(6,10),(7,8),(7,10),(8,10),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(2,3),(3,9),(4,9),(4,11),(4,12),(4,13),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,10),(6,12),(6,13),(7,8),(7,10),(7,11),(7,13),(8,10),(8,11),(8,12),(9,11),(9,12),(9,13),(10,11),(10,12),(10,13),(11,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
=> ([(2,3),(3,13),(4,5),(4,6),(4,11),(4,12),(4,13),(5,6),(5,10),(5,11),(5,13),(6,9),(6,11),(6,13),(7,8),(7,9),(7,10),(7,12),(7,13),(8,9),(8,10),(8,12),(8,13),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(2,3),(2,12),(3,11),(4,5),(4,6),(4,7),(4,8),(4,12),(5,6),(5,8),(5,10),(5,11),(6,8),(6,9),(6,11),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(2,3),(2,12),(3,11),(4,5),(4,6),(4,7),(4,8),(4,12),(5,6),(5,8),(5,10),(5,11),(6,8),(6,9),(6,11),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,5,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ([(2,3),(3,12),(4,7),(4,9),(4,11),(4,12),(5,6),(5,8),(5,10),(5,12),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(2,3),(2,11),(3,10),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,10),(6,7),(6,8),(6,11),(7,8),(7,9),(7,10),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,1,3,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(2,3),(3,11),(4,6),(4,9),(4,10),(4,11),(5,7),(5,8),(5,10),(5,11),(5,12),(6,8),(6,9),(6,10),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,11),(8,12),(9,10),(9,12),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,1,4,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ([(2,3),(3,12),(4,7),(4,9),(4,11),(4,12),(5,6),(5,8),(5,10),(5,12),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,10),(1,11),(1,12),(2,7),(2,11),(2,12),(3,7),(3,9),(3,10),(4,6),(4,10),(4,12),(5,6),(5,9),(5,11),(6,14),(7,13),(9,13),(9,14),(10,13),(10,14),(11,13),(11,14),(12,13),(12,14),(13,8),(14,8)],15)
=> ([(2,3),(2,14),(3,13),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(5,6),(5,7),(5,8),(5,10),(5,12),(5,13),(5,14),(6,7),(6,8),(6,10),(6,11),(6,13),(6,14),(7,8),(7,9),(7,11),(7,13),(7,14),(8,9),(8,12),(8,13),(8,14),(9,10),(9,11),(9,12),(9,13),(10,11),(10,12),(10,13),(11,12),(11,14),(12,14),(13,14)],15)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(2,3),(2,12),(3,11),(4,5),(4,6),(4,7),(4,8),(4,12),(5,6),(5,8),(5,10),(5,11),(6,8),(6,9),(6,11),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,4,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(2,3),(3,11),(4,6),(4,9),(4,10),(4,11),(5,7),(5,8),(5,10),(5,11),(5,12),(6,8),(6,9),(6,10),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,9),(8,11),(8,12),(9,10),(9,12),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,4,3,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(2,7),(3,6),(3,9),(4,5),(4,7),(4,8),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[3,1,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(2,7),(3,6),(3,9),(4,5),(4,7),(4,8),(5,8),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 1
Description
The number of maximally independent sets of vertices of a graph.
An '''independent set''' of vertices of a graph is a set of vertices no two of which are adjacent. If a set of vertices is independent then so is every subset. This statistic counts the number of maximally independent sets of vertices.
Matching statistic: St001311
Values
[1] => ([],1)
=> ([],1)
=> 0 = 1 - 1
[1,2] => ([(0,1)],2)
=> ([(0,1)],2)
=> 0 = 1 - 1
[2,1] => ([(0,1)],2)
=> ([(0,1)],2)
=> 0 = 1 - 1
[1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 0 = 1 - 1
[1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1 = 2 - 1
[2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1 = 2 - 1
[2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1 = 2 - 1
[3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1 = 2 - 1
[3,2,1] => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 0 = 1 - 1
[1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 0 = 1 - 1
[1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 3 = 4 - 1
[2,3,1,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
=> ? ∊ {8,8} - 1
[2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[3,1,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
=> ? ∊ {8,8} - 1
[3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 3 = 4 - 1
[3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 0 = 1 - 1
[1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 0 = 1 - 1
[1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(0,5),(0,8),(1,2),(1,3),(1,9),(2,4),(2,7),(3,7),(3,8),(4,6),(4,9),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ([(0,9),(0,11),(1,8),(1,10),(2,6),(2,7),(2,8),(2,10),(3,5),(3,7),(3,8),(3,10),(4,5),(4,6),(4,8),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,4,5,2] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,11),(0,12),(1,9),(1,10),(1,13),(2,7),(2,8),(2,11),(2,12),(3,6),(3,8),(3,11),(3,12),(4,5),(4,8),(4,11),(4,12),(5,9),(5,10),(5,13),(6,9),(6,10),(6,13),(7,9),(7,10),(7,13),(8,9),(8,13),(10,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ([(0,9),(0,11),(1,8),(1,10),(2,6),(2,7),(2,8),(2,10),(3,5),(3,7),(3,8),(3,10),(4,5),(4,6),(4,8),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,11),(0,12),(1,9),(1,10),(1,13),(2,7),(2,8),(2,11),(2,12),(3,6),(3,8),(3,11),(3,12),(4,5),(4,8),(4,11),(4,12),(5,9),(5,10),(5,13),(6,9),(6,10),(6,13),(7,9),(7,10),(7,13),(8,9),(8,13),(10,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ([(0,9),(0,10),(1,5),(1,6),(1,10),(2,3),(2,5),(2,6),(3,7),(3,8),(4,5),(4,6),(4,9),(4,10),(5,8),(6,7),(7,9),(7,10),(8,9),(8,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,5,3,2] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,3,4,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,3,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(0,6),(0,9),(1,3),(1,4),(1,5),(2,3),(2,4),(2,9),(3,8),(4,7),(5,7),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,4,3,5] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(0,5),(0,8),(1,2),(1,3),(1,9),(2,4),(2,7),(3,7),(3,8),(4,6),(4,9),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,4,5,3] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,2),(1,3),(1,6),(2,5),(2,7),(3,7),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(6,9),(6,10),(7,8),(8,9),(8,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,5,3,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,2),(1,3),(1,6),(2,5),(2,7),(3,7),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(6,9),(6,10),(7,8),(8,9),(8,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,5,4,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,1,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,1,5,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,2),(1,3),(1,6),(2,5),(2,7),(3,7),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(6,9),(6,10),(7,8),(8,9),(8,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,4,1,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,4,5,1] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(0,11),(0,12),(1,6),(1,7),(1,8),(2,7),(2,8),(2,10),(3,9),(3,11),(3,12),(4,5),(4,7),(4,8),(4,10),(5,9),(5,11),(5,12),(6,9),(6,11),(6,12),(7,12),(8,9),(9,10),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,5,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,11),(0,12),(1,9),(1,10),(1,13),(2,7),(2,8),(2,11),(2,12),(3,6),(3,8),(3,11),(3,12),(4,5),(4,8),(4,11),(4,12),(5,9),(5,10),(5,13),(6,9),(6,10),(6,13),(7,9),(7,10),(7,13),(8,9),(8,13),(10,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
=> ([(0,9),(0,13),(1,8),(1,11),(1,12),(2,4),(2,5),(2,13),(3,6),(3,7),(3,9),(3,13),(4,8),(4,10),(4,12),(5,8),(5,10),(5,11),(6,8),(6,10),(6,11),(6,12),(7,8),(7,10),(7,11),(7,12),(9,10),(9,11),(9,12),(10,13),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,5,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ([(0,10),(0,12),(1,9),(1,10),(1,12),(2,3),(2,8),(2,12),(3,6),(3,11),(4,5),(4,6),(4,11),(5,9),(5,10),(5,12),(6,8),(6,9),(7,8),(7,9),(7,10),(7,12),(8,11),(9,11),(10,11),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,1,3,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(0,11),(0,12),(1,6),(1,7),(1,8),(2,7),(2,8),(2,10),(3,9),(3,11),(3,12),(4,5),(4,7),(4,8),(4,10),(5,9),(5,11),(5,12),(6,9),(6,11),(6,12),(7,12),(8,9),(9,10),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,1,4,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ([(0,10),(0,12),(1,9),(1,10),(1,12),(2,3),(2,8),(2,12),(3,6),(3,11),(4,5),(4,6),(4,11),(5,9),(5,10),(5,12),(6,8),(6,9),(7,8),(7,9),(7,10),(7,12),(8,11),(9,11),(10,11),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,10),(1,11),(1,12),(2,7),(2,11),(2,12),(3,7),(3,9),(3,10),(4,6),(4,10),(4,12),(5,6),(5,9),(5,11),(6,14),(7,13),(9,13),(9,14),(10,13),(10,14),(11,13),(11,14),(12,13),(12,14),(13,8),(14,8)],15)
=> ([(0,13),(0,14),(1,5),(1,6),(1,14),(2,3),(2,4),(2,13),(3,10),(3,11),(3,12),(4,8),(4,9),(4,12),(5,9),(5,11),(5,12),(6,8),(6,10),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,13),(8,14),(9,13),(9,14),(10,13),(10,14),(11,13),(11,14)],15)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,4,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(0,11),(0,12),(1,6),(1,7),(1,8),(2,7),(2,8),(2,10),(3,9),(3,11),(3,12),(4,5),(4,7),(4,8),(4,10),(5,9),(5,11),(5,12),(6,9),(6,11),(6,12),(7,12),(8,9),(9,10),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,4,3,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[3,1,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 0 = 1 - 1
Description
The cyclomatic number of a graph.
This is the minimum number of edges that must be removed from the graph so that the result is a forest. This is also the first Betti number of the graph. It can be computed as $c + m - n$, where $c$ is the number of connected components, $m$ is the number of edges and $n$ is the number of vertices.
Matching statistic: St001317
Values
[1] => ([],1)
=> ([],1)
=> 0 = 1 - 1
[1,2] => ([(0,1)],2)
=> ([(0,1)],2)
=> 0 = 1 - 1
[2,1] => ([(0,1)],2)
=> ([(0,1)],2)
=> 0 = 1 - 1
[1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 0 = 1 - 1
[1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1 = 2 - 1
[2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1 = 2 - 1
[2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1 = 2 - 1
[3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1 = 2 - 1
[3,2,1] => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 0 = 1 - 1
[1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 0 = 1 - 1
[1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 3 = 4 - 1
[2,3,1,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
=> ? ∊ {8,8} - 1
[2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[3,1,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
=> ? ∊ {8,8} - 1
[3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 3 = 4 - 1
[3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 0 = 1 - 1
[1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 0 = 1 - 1
[1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(0,5),(0,8),(1,2),(1,3),(1,9),(2,4),(2,7),(3,7),(3,8),(4,6),(4,9),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ([(0,9),(0,11),(1,8),(1,10),(2,6),(2,7),(2,8),(2,10),(3,5),(3,7),(3,8),(3,10),(4,5),(4,6),(4,8),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,4,5,2] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,11),(0,12),(1,9),(1,10),(1,13),(2,7),(2,8),(2,11),(2,12),(3,6),(3,8),(3,11),(3,12),(4,5),(4,8),(4,11),(4,12),(5,9),(5,10),(5,13),(6,9),(6,10),(6,13),(7,9),(7,10),(7,13),(8,9),(8,13),(10,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ([(0,9),(0,11),(1,8),(1,10),(2,6),(2,7),(2,8),(2,10),(3,5),(3,7),(3,8),(3,10),(4,5),(4,6),(4,8),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,11),(0,12),(1,9),(1,10),(1,13),(2,7),(2,8),(2,11),(2,12),(3,6),(3,8),(3,11),(3,12),(4,5),(4,8),(4,11),(4,12),(5,9),(5,10),(5,13),(6,9),(6,10),(6,13),(7,9),(7,10),(7,13),(8,9),(8,13),(10,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ([(0,9),(0,10),(1,5),(1,6),(1,10),(2,3),(2,5),(2,6),(3,7),(3,8),(4,5),(4,6),(4,9),(4,10),(5,8),(6,7),(7,9),(7,10),(8,9),(8,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,5,3,2] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,3,4,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,3,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(0,6),(0,9),(1,3),(1,4),(1,5),(2,3),(2,4),(2,9),(3,8),(4,7),(5,7),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,4,3,5] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(0,5),(0,8),(1,2),(1,3),(1,9),(2,4),(2,7),(3,7),(3,8),(4,6),(4,9),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,4,5,3] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,2),(1,3),(1,6),(2,5),(2,7),(3,7),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(6,9),(6,10),(7,8),(8,9),(8,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,5,3,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,2),(1,3),(1,6),(2,5),(2,7),(3,7),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(6,9),(6,10),(7,8),(8,9),(8,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,5,4,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,1,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,1,5,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,2),(1,3),(1,6),(2,5),(2,7),(3,7),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(6,9),(6,10),(7,8),(8,9),(8,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,4,1,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,4,5,1] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(0,11),(0,12),(1,6),(1,7),(1,8),(2,7),(2,8),(2,10),(3,9),(3,11),(3,12),(4,5),(4,7),(4,8),(4,10),(5,9),(5,11),(5,12),(6,9),(6,11),(6,12),(7,12),(8,9),(9,10),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,5,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,11),(0,12),(1,9),(1,10),(1,13),(2,7),(2,8),(2,11),(2,12),(3,6),(3,8),(3,11),(3,12),(4,5),(4,8),(4,11),(4,12),(5,9),(5,10),(5,13),(6,9),(6,10),(6,13),(7,9),(7,10),(7,13),(8,9),(8,13),(10,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
=> ([(0,9),(0,13),(1,8),(1,11),(1,12),(2,4),(2,5),(2,13),(3,6),(3,7),(3,9),(3,13),(4,8),(4,10),(4,12),(5,8),(5,10),(5,11),(6,8),(6,10),(6,11),(6,12),(7,8),(7,10),(7,11),(7,12),(9,10),(9,11),(9,12),(10,13),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,5,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ([(0,10),(0,12),(1,9),(1,10),(1,12),(2,3),(2,8),(2,12),(3,6),(3,11),(4,5),(4,6),(4,11),(5,9),(5,10),(5,12),(6,8),(6,9),(7,8),(7,9),(7,10),(7,12),(8,11),(9,11),(10,11),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,1,3,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(0,11),(0,12),(1,6),(1,7),(1,8),(2,7),(2,8),(2,10),(3,9),(3,11),(3,12),(4,5),(4,7),(4,8),(4,10),(5,9),(5,11),(5,12),(6,9),(6,11),(6,12),(7,12),(8,9),(9,10),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,1,4,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ([(0,10),(0,12),(1,9),(1,10),(1,12),(2,3),(2,8),(2,12),(3,6),(3,11),(4,5),(4,6),(4,11),(5,9),(5,10),(5,12),(6,8),(6,9),(7,8),(7,9),(7,10),(7,12),(8,11),(9,11),(10,11),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,10),(1,11),(1,12),(2,7),(2,11),(2,12),(3,7),(3,9),(3,10),(4,6),(4,10),(4,12),(5,6),(5,9),(5,11),(6,14),(7,13),(9,13),(9,14),(10,13),(10,14),(11,13),(11,14),(12,13),(12,14),(13,8),(14,8)],15)
=> ([(0,13),(0,14),(1,5),(1,6),(1,14),(2,3),(2,4),(2,13),(3,10),(3,11),(3,12),(4,8),(4,9),(4,12),(5,9),(5,11),(5,12),(6,8),(6,10),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,13),(8,14),(9,13),(9,14),(10,13),(10,14),(11,13),(11,14)],15)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,4,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(0,11),(0,12),(1,6),(1,7),(1,8),(2,7),(2,8),(2,10),(3,9),(3,11),(3,12),(4,5),(4,7),(4,8),(4,10),(5,9),(5,11),(5,12),(6,9),(6,11),(6,12),(7,12),(8,9),(9,10),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,4,3,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[3,1,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 0 = 1 - 1
Description
The minimal number of occurrences of the forest-pattern in a linear ordering of the vertices of the graph.
A graph is a forest if and only if in any linear ordering of its vertices, there are no three vertices $a < b < c$ such that $(a,c)$ and $(b,c)$ are edges. This statistic is the minimal number of occurrences of this pattern, in the set of all linear orderings of the vertices.
Matching statistic: St001324
Values
[1] => ([],1)
=> ([],1)
=> 0 = 1 - 1
[1,2] => ([(0,1)],2)
=> ([(0,1)],2)
=> 0 = 1 - 1
[2,1] => ([(0,1)],2)
=> ([(0,1)],2)
=> 0 = 1 - 1
[1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 0 = 1 - 1
[1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1 = 2 - 1
[2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1 = 2 - 1
[2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1 = 2 - 1
[3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1 = 2 - 1
[3,2,1] => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 0 = 1 - 1
[1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 0 = 1 - 1
[1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 3 = 4 - 1
[2,3,1,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
=> ? ∊ {8,8} - 1
[2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[3,1,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
=> ? ∊ {8,8} - 1
[3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 3 = 4 - 1
[3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 0 = 1 - 1
[1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 0 = 1 - 1
[1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(0,5),(0,8),(1,2),(1,3),(1,9),(2,4),(2,7),(3,7),(3,8),(4,6),(4,9),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ([(0,9),(0,11),(1,8),(1,10),(2,6),(2,7),(2,8),(2,10),(3,5),(3,7),(3,8),(3,10),(4,5),(4,6),(4,8),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,4,5,2] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,11),(0,12),(1,9),(1,10),(1,13),(2,7),(2,8),(2,11),(2,12),(3,6),(3,8),(3,11),(3,12),(4,5),(4,8),(4,11),(4,12),(5,9),(5,10),(5,13),(6,9),(6,10),(6,13),(7,9),(7,10),(7,13),(8,9),(8,13),(10,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ([(0,9),(0,11),(1,8),(1,10),(2,6),(2,7),(2,8),(2,10),(3,5),(3,7),(3,8),(3,10),(4,5),(4,6),(4,8),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,11),(0,12),(1,9),(1,10),(1,13),(2,7),(2,8),(2,11),(2,12),(3,6),(3,8),(3,11),(3,12),(4,5),(4,8),(4,11),(4,12),(5,9),(5,10),(5,13),(6,9),(6,10),(6,13),(7,9),(7,10),(7,13),(8,9),(8,13),(10,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ([(0,9),(0,10),(1,5),(1,6),(1,10),(2,3),(2,5),(2,6),(3,7),(3,8),(4,5),(4,6),(4,9),(4,10),(5,8),(6,7),(7,9),(7,10),(8,9),(8,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,5,3,2] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,3,4,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,3,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(0,6),(0,9),(1,3),(1,4),(1,5),(2,3),(2,4),(2,9),(3,8),(4,7),(5,7),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,4,3,5] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(0,5),(0,8),(1,2),(1,3),(1,9),(2,4),(2,7),(3,7),(3,8),(4,6),(4,9),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,4,5,3] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,2),(1,3),(1,6),(2,5),(2,7),(3,7),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(6,9),(6,10),(7,8),(8,9),(8,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,5,3,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,2),(1,3),(1,6),(2,5),(2,7),(3,7),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(6,9),(6,10),(7,8),(8,9),(8,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,5,4,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,1,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,1,5,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,2),(1,3),(1,6),(2,5),(2,7),(3,7),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(6,9),(6,10),(7,8),(8,9),(8,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,4,1,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,4,5,1] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(0,11),(0,12),(1,6),(1,7),(1,8),(2,7),(2,8),(2,10),(3,9),(3,11),(3,12),(4,5),(4,7),(4,8),(4,10),(5,9),(5,11),(5,12),(6,9),(6,11),(6,12),(7,12),(8,9),(9,10),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,5,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,11),(0,12),(1,9),(1,10),(1,13),(2,7),(2,8),(2,11),(2,12),(3,6),(3,8),(3,11),(3,12),(4,5),(4,8),(4,11),(4,12),(5,9),(5,10),(5,13),(6,9),(6,10),(6,13),(7,9),(7,10),(7,13),(8,9),(8,13),(10,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
=> ([(0,9),(0,13),(1,8),(1,11),(1,12),(2,4),(2,5),(2,13),(3,6),(3,7),(3,9),(3,13),(4,8),(4,10),(4,12),(5,8),(5,10),(5,11),(6,8),(6,10),(6,11),(6,12),(7,8),(7,10),(7,11),(7,12),(9,10),(9,11),(9,12),(10,13),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,5,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ([(0,10),(0,12),(1,9),(1,10),(1,12),(2,3),(2,8),(2,12),(3,6),(3,11),(4,5),(4,6),(4,11),(5,9),(5,10),(5,12),(6,8),(6,9),(7,8),(7,9),(7,10),(7,12),(8,11),(9,11),(10,11),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,1,3,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(0,11),(0,12),(1,6),(1,7),(1,8),(2,7),(2,8),(2,10),(3,9),(3,11),(3,12),(4,5),(4,7),(4,8),(4,10),(5,9),(5,11),(5,12),(6,9),(6,11),(6,12),(7,12),(8,9),(9,10),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,1,4,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ([(0,10),(0,12),(1,9),(1,10),(1,12),(2,3),(2,8),(2,12),(3,6),(3,11),(4,5),(4,6),(4,11),(5,9),(5,10),(5,12),(6,8),(6,9),(7,8),(7,9),(7,10),(7,12),(8,11),(9,11),(10,11),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,10),(1,11),(1,12),(2,7),(2,11),(2,12),(3,7),(3,9),(3,10),(4,6),(4,10),(4,12),(5,6),(5,9),(5,11),(6,14),(7,13),(9,13),(9,14),(10,13),(10,14),(11,13),(11,14),(12,13),(12,14),(13,8),(14,8)],15)
=> ([(0,13),(0,14),(1,5),(1,6),(1,14),(2,3),(2,4),(2,13),(3,10),(3,11),(3,12),(4,8),(4,9),(4,12),(5,9),(5,11),(5,12),(6,8),(6,10),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,13),(8,14),(9,13),(9,14),(10,13),(10,14),(11,13),(11,14)],15)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,4,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(0,11),(0,12),(1,6),(1,7),(1,8),(2,7),(2,8),(2,10),(3,9),(3,11),(3,12),(4,5),(4,7),(4,8),(4,10),(5,9),(5,11),(5,12),(6,9),(6,11),(6,12),(7,12),(8,9),(9,10),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,4,3,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[3,1,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 0 = 1 - 1
Description
The minimal number of occurrences of the chordal-pattern in a linear ordering of the vertices of the graph.
A graph is chordal if and only if in any linear ordering of its vertices, there are no three vertices $a < b < c$ such that $(a,c)$ and $(b,c)$ are edges and $(a,b)$ is not an edge. This statistic is the minimal number of occurrences of this pattern, in the set of all linear orderings of the vertices.
Matching statistic: St001326
Values
[1] => ([],1)
=> ([],1)
=> 0 = 1 - 1
[1,2] => ([(0,1)],2)
=> ([(0,1)],2)
=> 0 = 1 - 1
[2,1] => ([(0,1)],2)
=> ([(0,1)],2)
=> 0 = 1 - 1
[1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 0 = 1 - 1
[1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1 = 2 - 1
[2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1 = 2 - 1
[2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1 = 2 - 1
[3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 1 = 2 - 1
[3,2,1] => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 0 = 1 - 1
[1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 0 = 1 - 1
[1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 3 = 4 - 1
[2,3,1,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
=> ? ∊ {8,8} - 1
[2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[3,1,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
=> ? ∊ {8,8} - 1
[3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 3 = 4 - 1
[3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 0 = 1 - 1
[1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 0 = 1 - 1
[1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(0,5),(0,8),(1,2),(1,3),(1,9),(2,4),(2,7),(3,7),(3,8),(4,6),(4,9),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ([(0,9),(0,11),(1,8),(1,10),(2,6),(2,7),(2,8),(2,10),(3,5),(3,7),(3,8),(3,10),(4,5),(4,6),(4,8),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,4,5,2] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,11),(0,12),(1,9),(1,10),(1,13),(2,7),(2,8),(2,11),(2,12),(3,6),(3,8),(3,11),(3,12),(4,5),(4,8),(4,11),(4,12),(5,9),(5,10),(5,13),(6,9),(6,10),(6,13),(7,9),(7,10),(7,13),(8,9),(8,13),(10,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ([(0,9),(0,11),(1,8),(1,10),(2,6),(2,7),(2,8),(2,10),(3,5),(3,7),(3,8),(3,10),(4,5),(4,6),(4,8),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,11),(0,12),(1,9),(1,10),(1,13),(2,7),(2,8),(2,11),(2,12),(3,6),(3,8),(3,11),(3,12),(4,5),(4,8),(4,11),(4,12),(5,9),(5,10),(5,13),(6,9),(6,10),(6,13),(7,9),(7,10),(7,13),(8,9),(8,13),(10,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ([(0,9),(0,10),(1,5),(1,6),(1,10),(2,3),(2,5),(2,6),(3,7),(3,8),(4,5),(4,6),(4,9),(4,10),(5,8),(6,7),(7,9),(7,10),(8,9),(8,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,4,5,3,2] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,3,4,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,3,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(0,6),(0,9),(1,3),(1,4),(1,5),(2,3),(2,4),(2,9),(3,8),(4,7),(5,7),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,4,3,5] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(0,5),(0,8),(1,2),(1,3),(1,9),(2,4),(2,7),(3,7),(3,8),(4,6),(4,9),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,4,5,3] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,2),(1,3),(1,6),(2,5),(2,7),(3,7),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(6,9),(6,10),(7,8),(8,9),(8,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,5,3,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,2),(1,3),(1,6),(2,5),(2,7),(3,7),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(6,9),(6,10),(7,8),(8,9),(8,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,1,5,4,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,1,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,1,5,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,2),(1,3),(1,6),(2,5),(2,7),(3,7),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(6,9),(6,10),(7,8),(8,9),(8,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,4,1,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,4,5,1] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(0,11),(0,12),(1,6),(1,7),(1,8),(2,7),(2,8),(2,10),(3,9),(3,11),(3,12),(4,5),(4,7),(4,8),(4,10),(5,9),(5,11),(5,12),(6,9),(6,11),(6,12),(7,12),(8,9),(9,10),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,3,5,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,11),(0,12),(1,9),(1,10),(1,13),(2,7),(2,8),(2,11),(2,12),(3,6),(3,8),(3,11),(3,12),(4,5),(4,8),(4,11),(4,12),(5,9),(5,10),(5,13),(6,9),(6,10),(6,13),(7,9),(7,10),(7,13),(8,9),(8,13),(10,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
=> ([(0,9),(0,13),(1,8),(1,11),(1,12),(2,4),(2,5),(2,13),(3,6),(3,7),(3,9),(3,13),(4,8),(4,10),(4,12),(5,8),(5,10),(5,11),(6,8),(6,10),(6,11),(6,12),(7,8),(7,10),(7,11),(7,12),(9,10),(9,11),(9,12),(10,13),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,5,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ([(0,10),(0,12),(1,9),(1,10),(1,12),(2,3),(2,8),(2,12),(3,6),(3,11),(4,5),(4,6),(4,11),(5,9),(5,10),(5,12),(6,8),(6,9),(7,8),(7,9),(7,10),(7,12),(8,11),(9,11),(10,11),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,1,3,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(0,11),(0,12),(1,6),(1,7),(1,8),(2,7),(2,8),(2,10),(3,9),(3,11),(3,12),(4,5),(4,7),(4,8),(4,10),(5,9),(5,11),(5,12),(6,9),(6,11),(6,12),(7,12),(8,9),(9,10),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,1,4,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ([(0,10),(0,12),(1,9),(1,10),(1,12),(2,3),(2,8),(2,12),(3,6),(3,11),(4,5),(4,6),(4,11),(5,9),(5,10),(5,12),(6,8),(6,9),(7,8),(7,9),(7,10),(7,12),(8,11),(9,11),(10,11),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,10),(1,11),(1,12),(2,7),(2,11),(2,12),(3,7),(3,9),(3,10),(4,6),(4,10),(4,12),(5,6),(5,9),(5,11),(6,14),(7,13),(9,13),(9,14),(10,13),(10,14),(11,13),(11,14),(12,13),(12,14),(13,8),(14,8)],15)
=> ([(0,13),(0,14),(1,5),(1,6),(1,14),(2,3),(2,4),(2,13),(3,10),(3,11),(3,12),(4,8),(4,9),(4,12),(5,9),(5,11),(5,12),(6,8),(6,10),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,13),(8,14),(9,13),(9,14),(10,13),(10,14),(11,13),(11,14)],15)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,4,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(0,11),(0,12),(1,6),(1,7),(1,8),(2,7),(2,8),(2,10),(3,9),(3,11),(3,12),(4,5),(4,7),(4,8),(4,10),(5,9),(5,11),(5,12),(6,9),(6,11),(6,12),(7,12),(8,9),(9,10),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[2,5,4,3,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[3,1,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30} - 1
[5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 0 = 1 - 1
Description
The minimal number of occurrences of the interval-pattern in a linear ordering of the vertices of the graph.
A graph is an interval graph if and only if in any linear ordering of its vertices, there are no three vertices $a < b < c$ such that $(a,c)$ is an edge and $(a,b)$ is not an edge. This statistic is the minimal number of occurrences of this pattern, in the set of all linear orderings of the vertices.
Matching statistic: St000910
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00209: Permutations —pattern poset⟶ Posets
St000910: Posets ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 25%
St000910: Posets ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 25%
Values
[1] => ([],1)
=> ? = 1
[1,2] => ([(0,1)],2)
=> 1
[2,1] => ([(0,1)],2)
=> 1
[1,2,3] => ([(0,2),(2,1)],3)
=> 1
[1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[3,2,1] => ([(0,2),(2,1)],3)
=> 1
[1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 4
[2,3,1,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ? ∊ {8,8}
[2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[3,1,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ? ∊ {8,8}
[3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 4
[3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5
[4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,4,5,2] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,5,3,2] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,3,4,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,3,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,4,3,5] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,4,5,3] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,5,3,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,5,4,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,1,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,1,5,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,4,1,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,4,5,1] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,5,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,5,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,1,3,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,1,4,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,10),(1,11),(1,12),(2,7),(2,11),(2,12),(3,7),(3,9),(3,10),(4,6),(4,10),(4,12),(5,6),(5,9),(5,11),(6,14),(7,13),(9,13),(9,14),(10,13),(10,14),(11,13),(11,14),(12,13),(12,14),(13,8),(14,8)],15)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,4,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,4,3,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
Description
The number of maximal chains of minimal length in a poset.
Matching statistic: St000456
Values
[1] => ([],1)
=> ([],1)
=> ? = 1
[1,2] => ([(0,1)],2)
=> ([(0,1)],2)
=> 1
[2,1] => ([(0,1)],2)
=> ([(0,1)],2)
=> 1
[1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1
[1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2
[2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2
[2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2
[3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2
[3,2,1] => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 1
[1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1
[1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 3
[1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 5
[1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 5
[1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 5
[1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 3
[2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 3
[2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[2,3,1,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 5
[2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 3
[2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
=> ? ∊ {8,8}
[2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 5
[3,1,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 5
[3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
=> ? ∊ {8,8}
[3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 3
[3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 5
[3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 3
[4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 3
[4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 5
[4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 5
[4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 5
[4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 3
[4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1
[1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 1
[1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(0,5),(0,8),(1,2),(1,3),(1,9),(2,4),(2,7),(3,7),(3,8),(4,6),(4,9),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ([(0,9),(0,11),(1,8),(1,10),(2,6),(2,7),(2,8),(2,10),(3,5),(3,7),(3,8),(3,10),(4,5),(4,6),(4,8),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,4,5,2] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,11),(0,12),(1,9),(1,10),(1,13),(2,7),(2,8),(2,11),(2,12),(3,6),(3,8),(3,11),(3,12),(4,5),(4,8),(4,11),(4,12),(5,9),(5,10),(5,13),(6,9),(6,10),(6,13),(7,9),(7,10),(7,13),(8,9),(8,13),(10,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ([(0,9),(0,11),(1,8),(1,10),(2,6),(2,7),(2,8),(2,10),(3,5),(3,7),(3,8),(3,10),(4,5),(4,6),(4,8),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,11),(0,12),(1,9),(1,10),(1,13),(2,7),(2,8),(2,11),(2,12),(3,6),(3,8),(3,11),(3,12),(4,5),(4,8),(4,11),(4,12),(5,9),(5,10),(5,13),(6,9),(6,10),(6,13),(7,9),(7,10),(7,13),(8,9),(8,13),(10,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ([(0,9),(0,10),(1,5),(1,6),(1,10),(2,3),(2,5),(2,6),(3,7),(3,8),(4,5),(4,6),(4,9),(4,10),(5,8),(6,7),(7,9),(7,10),(8,9),(8,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,4,5,3,2] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,3,4,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,3,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(0,6),(0,9),(1,3),(1,4),(1,5),(2,3),(2,4),(2,9),(3,8),(4,7),(5,7),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,4,3,5] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ([(0,5),(0,8),(1,2),(1,3),(1,9),(2,4),(2,7),(3,7),(3,8),(4,6),(4,9),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,4,5,3] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,2),(1,3),(1,6),(2,5),(2,7),(3,7),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(6,9),(6,10),(7,8),(8,9),(8,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,5,3,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,2),(1,3),(1,6),(2,5),(2,7),(3,7),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(6,9),(6,10),(7,8),(8,9),(8,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,1,5,4,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ([(0,5),(0,8),(1,4),(1,6),(2,6),(2,8),(3,4),(3,5),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,1,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,1,5,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,2),(1,3),(1,6),(2,5),(2,7),(3,7),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(6,9),(6,10),(7,8),(8,9),(8,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,4,1,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,4,5,1] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(0,11),(0,12),(1,6),(1,7),(1,8),(2,7),(2,8),(2,10),(3,9),(3,11),(3,12),(4,5),(4,7),(4,8),(4,10),(5,9),(5,11),(5,12),(6,9),(6,11),(6,12),(7,12),(8,9),(9,10),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,3,5,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ([(0,9),(0,10),(1,8),(1,10),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,8),(5,9),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,11),(0,12),(1,9),(1,10),(1,13),(2,7),(2,8),(2,11),(2,12),(3,6),(3,8),(3,11),(3,12),(4,5),(4,8),(4,11),(4,12),(5,9),(5,10),(5,13),(6,9),(6,10),(6,13),(7,9),(7,10),(7,13),(8,9),(8,13),(10,12),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
=> ([(0,9),(0,13),(1,8),(1,11),(1,12),(2,4),(2,5),(2,13),(3,6),(3,7),(3,9),(3,13),(4,8),(4,10),(4,12),(5,8),(5,10),(5,11),(6,8),(6,10),(6,11),(6,12),(7,8),(7,10),(7,11),(7,12),(9,10),(9,11),(9,12),(10,13),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,5,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ([(0,10),(0,12),(1,9),(1,10),(1,12),(2,3),(2,8),(2,12),(3,6),(3,11),(4,5),(4,6),(4,11),(5,9),(5,10),(5,12),(6,8),(6,9),(7,8),(7,9),(7,10),(7,12),(8,11),(9,11),(10,11),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,9),(0,10),(1,4),(1,7),(1,10),(2,3),(2,6),(2,9),(3,8),(3,11),(4,8),(4,11),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,1,3,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(0,11),(0,12),(1,6),(1,7),(1,8),(2,7),(2,8),(2,10),(3,9),(3,11),(3,12),(4,5),(4,7),(4,8),(4,10),(5,9),(5,11),(5,12),(6,9),(6,11),(6,12),(7,12),(8,9),(9,10),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,1,4,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ([(0,10),(0,12),(1,9),(1,10),(1,12),(2,3),(2,8),(2,12),(3,6),(3,11),(4,5),(4,6),(4,11),(5,9),(5,10),(5,12),(6,8),(6,9),(7,8),(7,9),(7,10),(7,12),(8,11),(9,11),(10,11),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,10),(1,11),(1,12),(2,7),(2,11),(2,12),(3,7),(3,9),(3,10),(4,6),(4,10),(4,12),(5,6),(5,9),(5,11),(6,14),(7,13),(9,13),(9,14),(10,13),(10,14),(11,13),(11,14),(12,13),(12,14),(13,8),(14,8)],15)
=> ([(0,13),(0,14),(1,5),(1,6),(1,14),(2,3),(2,4),(2,13),(3,10),(3,11),(3,12),(4,8),(4,9),(4,12),(5,9),(5,11),(5,12),(6,8),(6,10),(6,12),(7,8),(7,9),(7,10),(7,11),(7,12),(8,13),(8,14),(9,13),(9,14),(10,13),(10,14),(11,13),(11,14)],15)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ([(0,11),(0,12),(1,4),(1,5),(1,11),(2,3),(2,9),(2,12),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(6,12),(7,9),(7,11),(7,12),(8,9),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,4,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ([(0,11),(0,12),(1,6),(1,7),(1,8),(2,7),(2,8),(2,10),(3,9),(3,11),(3,12),(4,5),(4,7),(4,8),(4,10),(5,9),(5,11),(5,12),(6,9),(6,11),(6,12),(7,12),(8,9),(9,10),(10,11),(10,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[2,5,4,3,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,5),(0,9),(1,4),(1,8),(2,4),(2,7),(2,8),(3,5),(3,6),(3,9),(4,6),(5,7),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,7,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,14,14,14,14,16,16,16,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,26,26,26,26,26,26,26,26,28,28,30,30,30,30}
[5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 1
Description
The monochromatic index of a connected graph.
This is the maximal number of colours such that there is a colouring of the edges where any two vertices can be joined by a monochromatic path.
For example, a circle graph other than the triangle can be coloured with at most two colours: one edge blue, all the others red.
The following 11 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000086The number of subgraphs. St000450The number of edges minus the number of vertices plus 2 of a graph. St001510The number of self-evacuating linear extensions of a finite poset. St001398Number of subsets of size 3 of elements in a poset that form a "v". St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001656The monophonic position number of a graph. St000683The number of points below the Dyck path such that the diagonal to the north-east hits the path between two down steps, and the diagonal to the north-west hits the path between two up steps. St000980The number of boxes weakly below the path and above the diagonal that lie below at least two peaks. St001875The number of simple modules with projective dimension at most 1. St001669The number of single rises in a Dyck path.
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